LONDON (Reuters) - Uncertainty in the run-up to Britain's vote on its EU membership slowed service sector growth last month to a three-year low and sent business expectations to their weakest since the end of 2012, a survey showed on Tuesday.

The Markit/CIPS UK services PMI eased to 52.3 in June from 53.5 in May, matching April's level which was the lowest since April 2013. That was below a median forecast in a Reuters poll of economists for a 52.7 figure.

The vast majority of responses from services companies - 89 percent - were received before it became clear on June 24 that Britons had voted to leave the EU.

The result sparked pandemonium in Britain's two main political parties and sent sterling to a 31-year low against the dollar.

The PMI survey, along with similar ones for manufacturing and construction, pointed to economic growth of 0.2 percent in the second quarter down from 0.4 percent in the first three months of 2016. But that was unchanged from its outlook in May.

"A further slowing, and possible contraction, looks highly likely in coming months as a result of the uncertainty created by the EU referendum," said Chris Williamson, chief economist at

Markit, which compiles the survey. "More policy action is therefore likely in the coming weeks." Bank of England Governor Mark Carney on Thursday said the economic outlook had deteriorated and it would likely need

further stimulus over the summer.

Growth in services activity over the second quarter as a whole was the weakest since the first quarter of 2013, Markit said.

A measure of business expectations fell to 66.4 in June from 70.8, it was its lowest level since December 2012. Markit said firms reported that uncertainty linked to the EU referendum had weighed on their activity outlook for the coming twelve months.

Employment growth also eased to its weakest since mid-2013.

Markit's composite index, including activity in the manufacturing, services and construction sector, fell to 51.8 in June from 52.9 in May, its lowest since March 2013.

(Reporting by Ana Nicolaci da Costa; Editing by Hugh Lawson)